{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FI64XZPFKHRTUEV22RBEFWBVCO","short_pith_number":"pith:FI64XZPF","schema_version":"1.0","canonical_sha256":"2a3dcbe5e551e33a12bad44242d83513bde6735c391fcbc8d10abdbbf869625d","source":{"kind":"arxiv","id":"1512.02492","version":3},"attestation_state":"computed","paper":{"title":"Holomorphic field realization of SH$^c$ and quantum geometry of quiver gauge theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.QA","math.RT"],"primary_cat":"hep-th","authors_text":"Hong Zhang, Jean-Emile Bourgine, Yutaka Matsuo","submitted_at":"2015-12-08T14:54:11Z","abstract_excerpt":"In the context of 4D/2D dualities, SH$^c$ algebra, introduced by Schiffmann and Vasserot, provides a systematic method to analyse the instanton partition functions of $\\mathcal{N}=2$ supersymmetric gauge theories. In this paper, we rewrite the SH$^c$ algebra in terms of three holomorphic fields $D_0(z)$, $D_{\\pm1}(z)$ with which the algebra and its epresentations are simplified. The instanton partition functions for arbitrary $\\mathcal{N}=2$ super Yang-Mills theories with $A_n$ and $A^{(1)}_n$ type quiver diagrams are compactly expressed as a product of four building blocks: Gaiotto state, dil"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.02492","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-08T14:54:11Z","cross_cats_sorted":["math-ph","math.AG","math.MP","math.QA","math.RT"],"title_canon_sha256":"73d02216bceb0d1f7a91ee3fd104885151659d5603181b1326f0196febd27aae","abstract_canon_sha256":"2d9a77b377b39d29789596cd05f017d5cd4990177532bc746cd52908d4e137fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:01.853254Z","signature_b64":"hKZepHvK/iQu6BKPTxLjNWmZUbPbZl8N1DDi0zUqjZmj6nuA6cp2MPFBYJp+Aw0sqt0r88Dy1cUhj1MBYMGMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a3dcbe5e551e33a12bad44242d83513bde6735c391fcbc8d10abdbbf869625d","last_reissued_at":"2026-05-18T01:14:01.852717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:01.852717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Holomorphic field realization of SH$^c$ and quantum geometry of quiver gauge theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.QA","math.RT"],"primary_cat":"hep-th","authors_text":"Hong Zhang, Jean-Emile Bourgine, Yutaka Matsuo","submitted_at":"2015-12-08T14:54:11Z","abstract_excerpt":"In the context of 4D/2D dualities, SH$^c$ algebra, introduced by Schiffmann and Vasserot, provides a systematic method to analyse the instanton partition functions of $\\mathcal{N}=2$ supersymmetric gauge theories. In this paper, we rewrite the SH$^c$ algebra in terms of three holomorphic fields $D_0(z)$, $D_{\\pm1}(z)$ with which the algebra and its epresentations are simplified. The instanton partition functions for arbitrary $\\mathcal{N}=2$ super Yang-Mills theories with $A_n$ and $A^{(1)}_n$ type quiver diagrams are compactly expressed as a product of four building blocks: Gaiotto state, dil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02492","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.02492","created_at":"2026-05-18T01:14:01.852800+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02492v3","created_at":"2026-05-18T01:14:01.852800+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02492","created_at":"2026-05-18T01:14:01.852800+00:00"},{"alias_kind":"pith_short_12","alias_value":"FI64XZPFKHRT","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FI64XZPFKHRTUEV2","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FI64XZPF","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2512.07758","citing_title":"Charge functions for odd dimensional partitions","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FI64XZPFKHRTUEV22RBEFWBVCO","json":"https://pith.science/pith/FI64XZPFKHRTUEV22RBEFWBVCO.json","graph_json":"https://pith.science/api/pith-number/FI64XZPFKHRTUEV22RBEFWBVCO/graph.json","events_json":"https://pith.science/api/pith-number/FI64XZPFKHRTUEV22RBEFWBVCO/events.json","paper":"https://pith.science/paper/FI64XZPF"},"agent_actions":{"view_html":"https://pith.science/pith/FI64XZPFKHRTUEV22RBEFWBVCO","download_json":"https://pith.science/pith/FI64XZPFKHRTUEV22RBEFWBVCO.json","view_paper":"https://pith.science/paper/FI64XZPF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02492&json=true","fetch_graph":"https://pith.science/api/pith-number/FI64XZPFKHRTUEV22RBEFWBVCO/graph.json","fetch_events":"https://pith.science/api/pith-number/FI64XZPFKHRTUEV22RBEFWBVCO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FI64XZPFKHRTUEV22RBEFWBVCO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FI64XZPFKHRTUEV22RBEFWBVCO/action/storage_attestation","attest_author":"https://pith.science/pith/FI64XZPFKHRTUEV22RBEFWBVCO/action/author_attestation","sign_citation":"https://pith.science/pith/FI64XZPFKHRTUEV22RBEFWBVCO/action/citation_signature","submit_replication":"https://pith.science/pith/FI64XZPFKHRTUEV22RBEFWBVCO/action/replication_record"}},"created_at":"2026-05-18T01:14:01.852800+00:00","updated_at":"2026-05-18T01:14:01.852800+00:00"}